# Triangle Angle Calculator

URL: https://speedycalculator.com/calculators/math/triangle-angle/
Last updated: 2026-10-30

> The triangle angle calculator finds all three angles of a triangle from its three sides, from two sides and the included angle, or from two angles.

## Inputs

- What do you know?
- Side a (cm, m, mm, in, ft, yd, km, mi)
- Side b (cm, m, mm, in, ft, yd, km, mi)
- Side c (cm, m, mm, in, ft, yd, km, mi)
- Angle γ (between a and b) (°, rad, π rad, grad, turn)
- Angle α (°, rad, π rad, grad, turn)
- Angle β (°, rad, π rad, grad, turn)

## Results

- Angle α (opposite a)
- Angle β (opposite b)
- Angle γ (opposite c)
- Type by angles

## Formula

```
α = arccos((b² + c² − a²)/(2bc)),  α + β + γ = 180°
```

## Explanation

The angles of a triangle always add up to 180°. Knowing them is essential when cutting roof rafters, laying out triangular structures or checking whether a triangle is acute, right or obtuse.

### How to use the Triangle Angle Calculator

- **What do you know?**
- **Side a**
- **Side b**
- **Side c**
- **Angle γ (between a and b)**
- **Angle α**
- **Angle β**

Results update as you type, and everything is calculated in your browser.

### How it works

With three sides each angle comes from the law of cosines. With two sides and the included angle, the third side is computed first. With two angles, the third is 180° minus their sum.

### Inputs explained

FieldWhat to enterWhat do you know?Choose one: Three sides (SSS), Two sides and the angle between them (SAS), Two anglesSide aUnits: cm, m, mm, in, ft, yd …Side bUnits: cm, m, mm, in, ft, yd …Side cUnits: cm, m, mm, in, ft, yd …Angle γ (between a and b)Units: °, rad, π rad, grad, turnAngle αUnits: °, rad, π rad, grad, turnAngle βUnits: °, rad, π rad, grad, turn

### Example values

How the main result changes when **Side a** changes and everything else stays at the example values above:

Side a (cm)Angle α (opposite a) (°)2.520.36413.7532.3822544.41536.2556.84717.569.985310100.2866

## Worked example

Inputs — What do you know?: Three sides (SSS); Side a: 5 cm; Side b: 6 cm; Side c: 7 cm.

Results — **Angle α (opposite a) = 44.415309 °**; Angle β (opposite b) = 57.12165 °; Angle γ (opposite c) = 78.463041 °; Type by angles = Acute.

## Key terms

- **Interior angle**: An angle inside the triangle at a vertex.

## FAQ

**Why do triangle angles add to 180°?**
A line through one vertex parallel to the opposite side shows the three angles form a straight angle.

**Can a triangle have two right angles?**
No – the third angle would be 0°.

**How do I find an angle from three sides?**
Use the law of cosines solved for the angle.

**What is an exterior angle?**
180° minus an interior angle; it equals the sum of the two remote interior angles.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Triangle](https://mathworld.wolfram.com/Triangle.html)